sfr renamed as lbotr and its symbol changed according to lsubr

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / ldrop_sfr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_sfr.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_sfr.ma
deleted file mode 100644 (file)
index 9d4cc31..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_sfr.ma
+++ /dev/null
@@ -1,94 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/substitution/lsubr_sfr.ma".
-include "basic_2/substitution/ldrop_ldrop.ma".
-
-(* DROPPING *****************************************************************)
-
-(* Inversion lemmas about local env. full refinement for substitution *******)
-
-(* Note: ldrop_ldrop not needed *)
-lemma sfr_inv_ldrop: ∀I,L,K,V,i. ⇩[0, i] L ≡ K. ⓑ{I}V → ∀d,e. ≽ [d, e] L →
-                     d ≤ i → i < d + e → I = Abbr.
-#I #L elim L -L
-[ #K #V #i #H
-  lapply (ldrop_inv_atom1 … H) -H #H destruct
-| #L #J #W #IHL #K #V #i #H
-  elim (ldrop_inv_O1 … H) -H *
-  [ -IHL #H1 #H2 #d #e #HL #Hdi #Hide destruct
-    lapply (le_n_O_to_eq … Hdi) -Hdi #H destruct
-    lapply (HL … (L.ⓓW) ?) -HL /2 width=1/ #H
-    elim (lsubr_inv_abbr2 … H ?) -H // -Hide #K #_ #H destruct //
-  | #Hi #HLK #d @(nat_ind_plus … d) -d
-    [ #e #H #_ #Hide
-      elim (sfr_inv_bind … H ?) -H [2: /2 width=2/ ] #HL #H destruct
-      @(IHL … HLK … HL) -IHL -HLK -HL // /2 width=1/
-    | #d #_ #e #H #Hdi #Hide
-      lapply (sfr_inv_skip … H ?) -H // #HL
-      @(IHL … HLK … HL) -IHL -HLK -HL /2 width=1/
-    ]
-  ]
-]
-qed-.
-
-(* Properties about local env. full refinement for substitution *************)
-
-(* Note: ldrop_ldrop not needed *)
-lemma sfr_ldrop: ∀L,d,e.
-                 (∀I,K,V,i. d ≤ i → i < d + e → ⇩[0, i] L ≡ K. ⓑ{I}V → I = Abbr) →
-                 ≽ [d, e] L.
-#L elim L -L //
-#L #I #V #IHL #d @(nat_ind_plus … d) -d
-[ #e @(nat_ind_plus … e) -e //
-  #e #_ #H0
-  >(H0 I L V 0 ? ? ?) //
-  /5 width=6 by sfr_abbr, ldrop_ldrop, lt_minus_to_plus_r/ (**) (* auto now too slow without trace *)
-| #d #_ #e #H0
-  /5 width=6 by sfr_skip, ldrop_ldrop, le_S_S, lt_minus_to_plus_r/ (**) (* auto now too slow without trace *)
-]
-qed.
-
-lemma sfr_ldrop_trans_le: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ∀dd,ee. ≽ [dd, ee] L1 →
-                          dd + ee ≤ d → ≽ [dd, ee] L2.
-#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hddee
-@sfr_ldrop #I #K2 #V2 #i #Hddi #Hiddee #HLK2
-lapply (lt_to_le_to_lt … Hiddee Hddee) -Hddee #Hid
-elim (ldrop_trans_le … HL12 … HLK2 ?) -L2 /2 width=2/ #X #HLK1 #H
-elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ -Hid #K1 #V1 #HK12 #HV21 #H destruct
-@(sfr_inv_ldrop … HLK1 … HL1) -L1 -K1 -V1 //
-qed.
-
-lemma sfr_ldrop_trans_be_up: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 →
-                             ∀dd,ee. ≽ [dd, ee] L1 →
-                             dd ≤ d + e → d + e ≤ dd + ee →
-                             ≽ [d, dd + ee - d - e] L2.
-#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hdde #Hddee
-@sfr_ldrop #I #K2 #V2 #i #Hdi #Hiddee #HLK2
-lapply (transitive_le ? ? (i+e)… Hdde ?) -Hdde /2 width=1/ #Hddie
->commutative_plus in Hiddee; >minus_minus_comm <plus_minus_m_m /2 width=1/ -Hddee #Hiddee
-lapply (ldrop_trans_ge … HL12 … HLK2 ?) -L2 // -Hdi  #HL1K2
-@(sfr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus // -Hddie /2 width=1/
-qed.
-
-lemma sfr_ldrop_trans_ge: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ∀dd,ee. ≽ [dd, ee] L1 →
-                          d + e ≤ dd → ≽ [dd - e, ee] L2.
-#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hddee
-@sfr_ldrop #I #K2 #V2 #i #Hddi #Hiddee #HLK2
-elim (le_inv_plus_l … Hddee) -Hddee #Hdde #Hedd
->plus_minus in Hiddee; // #Hiddee
-lapply (transitive_le … Hdde Hddi) -Hdde #Hid
-lapply (ldrop_trans_ge … HL12 … HLK2 ?) -L2 // -Hid #HL1K2
-@(sfr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus /2 width=1/
-qed.